a/Faraday on a British ban-
knote.
b/Faraday’s experiment, sim-
plified and shown with modern
equipment.
ture of 19th century England. Faraday, working in 1831, had only a
vague and general idea that electricity and magnetism were related
to each other, based on Oersted’s demonstration, a decade before,
that magnetic fields were caused by electric currents.
Figure b is a simplified drawing of the following experiment, as
described in Faraday’s original paper: “Two hundred and three feet
of copper wire... were passed round a large block of wood; [another]
two hundred and three feet of similar wire were interposed as a spiral
between the turns of the first, and metallic contact everywhere pre-
vented by twine [insulation]. One of these [coils] was connected with
a galvanometer [voltmeter], and the other with a battery... When
the contact was made, there was a sudden and very slight effect at
the galvanometer, and there was also a similar slight effect when
the contact with the battery was broken. But whilst the... current
was continuing to pass through the one [coil], no... effect... upon
the other [coil] could be perceived, although the active power of the
battery was proved to be great, by its heating the whole of its own
coil [through ordinary resistive heating]... ”
From Faraday’s notes and publications, it appears that the situ-
ation in figure b/3 was a surprise to him, and he probably thought
it would be a surprise to his readers, as well. That’s why he offered
evidence that the current was still flowing: to show that the bat-
tery hadn’t just died. The induction effect occurred during the short
time it took for the black coil’s magnetic field to be established, b/2.
Even more counterintuitively, we get an effect, equally strong but in
the opposite direction, when the circuit isbroken, b/4. The effect
occurs only when the magnetic field is changing, and it appears to
be proportional to the derivative∂B/∂t, which is in one direction
when the field is being established, and in the opposite direction
when it collapses.
The effect is proportional to∂B/∂t, but whatisthe effect? A
voltmeter is nothing more than a resistor with an attachment for
measuring the current through it. A current will not flow through
a resistor unless there is some electric field pushing the electrons,
so we conclude that the changingmagnetic fieldhas produced an
electric fieldin the surrounding space. Since the white wire is not
a perfect conductor, there must be electric fields in it as well. The
remarkable thing about the circuit formed by the white wire is that
as the electrons travel around and around, they are always being
pushed forward by electric fields. This violates the loop rule, which
says that when an electron makes a round trip, there is supposed
to be just as much “uphill” (moving against the electric field) as
“downhill” (moving with it). That’s OK. The loop rule is only true
for statics. Faraday’s experiments show that an electron really can
go around and around, and always be going “downhill,” as in the
famous drawing by M.C. Escher shown in figure c. That’s just what
happens when you have a curly field.712 Chapter 11 Electromagnetism